## Introduction to statistical data analysis

August 27, 2011 at 01:55 PM | categories: data analysis | View Comments

## Contents

## Introduction to statistical data analysis

```
clear all
clc
```

## Problem statement.

Given several measurements of a single quantity, determine the average value of the measurements, the standard deviation of the measurements and the 95% confidence interval for the average.

## the data

y = [8.1 8.0 8.1];

## the average and standard deviation

ybar = mean(y) s = std(y)

ybar = 8.0667 s = 0.0577

## the confidence interval

This is a recipe for computing the confidence interval. The strategy is:

- compute the average
- Compute the standard deviation of your data
- Define the confidence interval, e.g. 95% = 0.95
- compute the student-t multiplier. This is a function of the confidence interval you specify, and the number of data points you have minus 1. You subtract 1 because one degree of freedom is lost from calculating the average.

The confidence interval is defined as ybar +- T_multiplier*std/sqrt(n).

the tinv command provides the T_multiplier

ci = 0.95; alpha = 1 - ci; n = length(y); %number of elements in the data vector T_multiplier = tinv(1-alpha/2, n-1) % the multiplier is large here because there is so little data. That means % we do not have a lot of confidence on the true average or standard % deviation ci95 = T_multiplier*s/sqrt(n) % confidence interval sprintf('The confidence interval is %1.1f +- %1.1f',ybar,ci95) [ybar - ci95, ybar + ci95] % we can say with 95% confidence that the true mean lies between these two % values. % categories: Data analysis

T_multiplier = 4.3027 ci95 = 0.1434 ans = The confidence interval is 8.1 +- 0.1 ans = 7.9232 8.2101